1. Field of the Invention
The present invention relates to a coding method. More particularly, the present invention relates to a coding method for reducing the number of paths in a state transition of a code sequence.
2. Description of the Related Art
A CCK (Complementary Code Keying) method is one of the typical coding methods. The CCK method employs a code vector C represented by the following equation (1):                                                         C              =                            ⁢                              {                                                      C                    1                                    ,                                      C                    2                                    ,                                      C                    3                                    ,                                      C                    4                                    ,                                      C                    5                                    ,                                      C                    6                                    ,                                      C                    7                                    ,                                      C                    8                                                  }                                                                                        =                            ⁢                              {                                                      ⅇ                                          j                      ⁢                                                                                           ⁢                                              (                                                                              p                            1                                                    +                                                      p                            2                                                    +                                                      p                            3                                                    +                                                      p                            4                                                                          )                                                                              ,                                      ⅇ                                          j                      ⁢                                                                                           ⁢                                              (                                                                              p                            1                                                    +                                                      p                            3                                                    +                                                      p                            4                                                                          )                                                                              ,                                      ⅇ                                          j                      ⁢                                                                                           ⁢                                              (                                                                              p                            1                                                    +                                                      p                            2                                                    +                                                      p                            4                                                                          )                                                                              ,                                                                                                                                        ⁢                                                      -                                          ⅇ                                              j                        ⁢                                                                                                   ⁢                                                  (                                                                                    p                              1                                                        +                                                          p                              4                                                                                )                                                                                                      ,                                      ⅇ                                          j                      ⁢                                                                                           ⁢                                              (                                                                              p                            1                                                    +                                                      p                            2                                                    +                                                      p                            3                                                                          )                                                                              ,                                      ⅇ                                          j                      ⁡                                              (                                                                              p                            1                                                    +                                                      p                            3                                                                          )                                                                              ,                                      -                                          ⅇ                                              j                        ⁢                                                                                                   ⁢                                                  (                                                                                    p                              1                                                        +                                                          p                              2                                                                                )                                                                                                      ,                                      ⅇ                                          j                      ⁢                                                                                           ⁢                                              p                        1                                                                                            }                            .                                                          (        1        )            Here, p1, p2, p3 and p4 are phases that are respectively determined by two-symbol data. That is, the code vector C includes an 8-symbol data. A set of the code vectors constitutes the Euclidean geometry space.
From the equation (1), C4 is represented by the following equation:                               C          4                =                  -                                                                      C                  2                                ⁢                                  C                  3                                                            C                1                                      .                                              (        2        )            C4 is uniquely determined when C1, C2 and C3 are determined, that is, C4 is an insertion code uniquely determined by a subset including input codes C1, C2 and C3 of a set {Ck} (k is an integer between 1 and 8).
Moreover, if C5 is determined, C6, C7 and C8 are uniquely determined from the following equation:                                           C            6                    =                                                    C                2                            ⁢                              C                5                                                    C              1                                      ,                              C            7                    =                      -                                                            C                  3                                ⁢                                  C                  5                                                            C                1                                                    ,                              C            8                    =                                                                      C                  2                                ⁢                                  C                  3                                ⁢                                  C                  5                                                            C                1                2                                      .                                              (        3        )            C6, C7 and C8 are insertion codes uniquely determined by C1, C2, C3 and C5.
Let us consider a case that a code coded by CCK method is decoded by a maximum likelihood sequence detection (MLSD) method assuming a trellis memory length to be 3. Here, it is also assumed that each of the codes C1, C2, . . . , C8 is a four-value code having any value of ±1 and ±j.
FIG. 1 is a trellis chart showing a state transition in this case. If the trellis memory length is 3, one state is determined by two continuous codes CJ and CJ+1 and the other state is determined by Cj+1 and Cj+2. Thus, the transition from one state to the other state is determined by three continuous codes. Hereafter, a set consisting of all states determined by the codes Cj and Cj+1 are noted as a state group {Cj+1, Cj}. Also, a state of Cj+1=α and Cj=β is noted as a state (α, β). Here, both α and β have any value of ±1 and ±j. Therefore, the state group {Cj+1, Cj} is constituted by 16 states.
Also, a path from a state (α1, β1) in the state group {Cj+1, CJ} to a state (α2, β2) in the state group {Cj+2, CJ+1} is hereinafter noted as a path (α1, β1)→(α2, β2).
When the code coded by using CCK is decoded by the maximum likelihood sequence detection (MLSD) method, a transition to one of states belonging to a state group {C2, C1} is done from four states belonging to a state group {C1, C0}. That is, there are four paths reaching one state of the state group {C2, C1}. For example, let us consider a path reaching a state (1,1) in the state group {C2, C1} from any states included in the state group {C1, C0}. As the path reaching the state (1,1) of the state group {C2, C1}, there are four paths of a path (1,1)→(1,1), a path (1,j)→(1,1), a path (1,−1)→(1,1) and a path (1,−j)→(1,1). When the code coded by using CCK is decoded, the maximum likelihood path is selected from the four paths. Similarly, there are four paths reaching one state in the state group {C3, C2}. Then, the maximum likelihood path is selected from the four paths.
On the other hand, there is only one path reaching one state in the state group {C4, C3} because of the existence of the relation of the equation (2). That is, each of the states included in the state group {C2, C1} corresponds to one of the states included in the state group {C2, C1}. In this way, the number of paths reaching one state in the state group {C4, C3} is limited to a quarter of the number of paths reaching one state in the state group {C2, C1} and the state group {C3, C2}. Thus, a metric between paths is extended to thereby reduce a probability of an selection error of a path.
In the coding method, a portion in which a coding gain is practically used is C4, C6, C7 and C8 in the code vector C. Thus, there is the deviation in the portion in which the coding gain is practically used. This results from the fact that a system estimation is carried out by using the state transition determined by the trellis memory length shorter than the number of symbols serving as a unit.
Moreover, if the number of previous input codes determining the state transition is greater than a trellis memory length, an irregularity is induced in which there are a plurality of paths reaching a certain state, and on the other hand, there is no path reaching a certain state. The coding method having such deviation and irregularity is not optimal.
It is desired that the path is regularly reduced without any deviation, the existence of the path is not irregular and the code gain is effectively used.
Other coding methods are disclosed in Japanese Laid Open Patent Application (Jp-A-Heisei 10-134521 and Jp-A-Heisei 11-186917), which may be related to the present invention described below. However, both of the other coding methods does not teach a technique reducing the deviation and irregularity in the generated codes.